single-session analysis
TRANSCRIPT
![Page 1: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/1.jpg)
GLM
Design matrix
Voxel time-series data
timetime
Voxel-wise single-subject analysis
Preprocesseddata
FMRI data
Single-subjecteffect sizestatistics
time
Stimulus/tasktimings
Motion correctionHigh-pass filteringSpatial smoothing
time
Effect sizestatistics
Statistic ImageSignificant
voxels/clusters
Contrast
Thresholding
Single-Session Analysis
![Page 2: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/2.jpg)
FMRI Modelling and Statistics
• An example experiment • Multiple regression (GLM) • T and F Contrasts• Null hypothesis testing• The residuals• Thresholding: multiple comparison
correction
![Page 3: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/3.jpg)
Two different views of the data
Time
A “smallish” number of volumes
...
A large number of time series
![Page 4: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/4.jpg)
FMRI Modelling and Statistics
• An example experiment• Multiple regression (GLM) • T and F Contrasts• Null hypothesis testing• The residuals• Thresholding: multiple comparison
correction
![Page 5: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/5.jpg)
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation
Scanner
Bed
Healthy Volunteer
+
Screen
![Page 6: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/6.jpg)
Car
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation
Screen
Noun is presented
Drive
Verb is generated
Scanner
Bed
Healthy Volunteer
![Page 7: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/7.jpg)
Door
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation
Screen
Noun is presented
Open
Verb is generated
Scanner
Bed
Healthy Volunteer
![Page 8: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/8.jpg)
Walk
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing
Screen
Verb is presented
Walk
Verb is repeated
Scanner
Bed
Healthy Volunteer
![Page 9: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/9.jpg)
Read
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing
Screen
Verb is presented
Read
Verb is repeated
Scanner
Bed
Healthy Volunteer
![Page 10: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/10.jpg)
+
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing• 3rd type: Null event
Screen
Crosshair is shown
Scanner
Bed
Healthy Volunteer
![Page 11: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/11.jpg)
+
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing• 3rd type: Null event
Screen
Crosshair is shownzz
zzzzzzzz
Scanner
Bed
Healthy Volunteer
![Page 12: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/12.jpg)
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing• 3rd type: Null event• 6 sec ISI, random order
Screen
+Scanner
Bed
Healthy Volunteer
![Page 13: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/13.jpg)
DriveReadOpenWalk
WalkDoor+Etc...Car
An example experimentAn FMRI adaptation of a classical PET experiment
• Three types of events• 1st type: Word Generation• 2nd type: Word Shadowing• 3rd type: Null event• 6 sec ISI, random order• For 24 events of each type
Screen
Read+++Scanner
Bed
Healthy Volunteer
![Page 14: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/14.jpg)
FMRI Modelling and Statistics
• An example experiment • Multiple regression (GLM) • T and F Contrasts• Null hypothesis testing• The residuals• Thresholding: multiple comparison
correction
![Page 15: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/15.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
![Page 16: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/16.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
First 100 seconds
Stick-function at each occurrence of a “generation event”
...
Well, hardly like this...
![Page 17: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/17.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
First 100 seconds
That looks better!
⊗ =HRF
=First 100 seconds
predicted response
![Page 18: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/18.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
445 seconds
⊗ =HRF
=
And this is the prediction for the whole time-series
445 seconds
![Page 19: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/19.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
So, if we spot a time-series like this
445 seconds
+
prediction
![Page 20: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/20.jpg)
Building a model
Our task is now to build a model for that experiment
What is our predicted response to the word generation events?
And then check it against our prediction we can conclude that this pixel is into word generation
445 seconds
+
prediction
![Page 21: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/21.jpg)
Building a model
Our task is now to build a model for that experiment
And we can do the same for the word shadowing events?
This time we used the onset times for the shadowing events to get the predicted brain response for those
445 secondsprediction
445 seconds
⊗ =
=
![Page 22: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/22.jpg)
Building a model
Our task is now to build a model for that experiment
And we can do the same for the word shadowing events?
And we can look for voxels that match that
445 seconds
+
prediction
![Page 23: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/23.jpg)
Formalising it: Multiple regression
+
Observed data
≈ β1· + β2·
Predicted responses
“Regressors”
Word Generation
Word Shadowing
Unknown “parameters”
![Page 24: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/24.jpg)
Slight detour: Making regressors
Event timings at “high” resolution
⊗ Convolve with HRF
Predictions at “high” resolution
Sub-sample at TR of experiment
Regressor
![Page 25: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/25.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·
Word Generation
Word Shadowing
0.5 0.5Let’s try these
parameter values
![Page 26: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/26.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·
Word Generation
Word Shadowing
0.5 0.5Hmm, not a
great fit
![Page 27: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/27.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·
Word Generation
Word Shadowing
0 1Oh dear,
even worse
![Page 28: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/28.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·
Word Generation
Word Shadowing
1.04 -0.10But that looks
good
![Page 29: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/29.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·1.10 1.02
And different voxels yield different parameters
![Page 30: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/30.jpg)
Estimation: Finding the “best” parameter values
• The estimation entails finding the parameter values such that the linear combination ”best” fits the data.
+
≈ β1· + β2·-0.04 -0.03
And different voxels yield different parameters
![Page 31: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/31.jpg)
�2
/stats/pe2
�1
/stats/pe1
�1.04�.10
�
�1.101.02
�
One model to fit them all
Time
Model
��.04�.03
�
![Page 32: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/32.jpg)
�
And we can also estimate the residual error
Residual errors
Difference between data and best fit: “Residual error”
![Page 33: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/33.jpg)
�2
/stats/pe2
�1
/stats/pe1
�1.04�.10
�
�1.101.02
�
Time
Model
��.04�.03
�
And we can also estimate the residual error
�2
/stats/sigmasquareds
![Page 34: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/34.jpg)
• The “Model” consists of a set of “regressors” i.e. tentative time series that we expect to see as a response to our stimulus
• The model typically consists of our stimulus functions convolved by the HRF
• The estimation entails finding the parameter values such that the linear combination of regressors ”best” fits the data
• Every voxel has its own unique parameter values, that is how a single model can fit so many different time series
• We can also get an estimate of the error through the “residuals”
Summary of what we learned so far
![Page 35: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/35.jpg)
= X �
��1
�2
�
+
General Linear Model (GLM) • This is placed into the General Linear Model (GLM) framework
Gaussian noise (temporal autocorrelation)Design MatrixData from
a voxel
Regressor, Explanatory Variable (EV)
Regression parameters, Effect sizes
y
=
e
+
x1 x2
![Page 36: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/36.jpg)
•The mean value is uninteresting in an FMRI session
• There are two equivalent options:
1.remove the mean from the data and don’t model it
2.put a term into the model to account for the mean
“Demeaning” and the GLM
In FSL we use option #1 for first-level analyses and #2 for higher-level analyses
A consequence is that the baseline condition in first-level analysis is NOT explicitly modelled (in FSL)
option #1
option #2
![Page 37: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/37.jpg)
FMRI Modelling and Statistics
• An example experiment• Multiple regression (GLM) • T and F Contrasts• Null hypothesis testing• The residuals• Thresholding: multiple comparison
correction
![Page 38: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/38.jpg)
• A contrast of parameter estimates (COPE) is a linear combination of PEs:
[1 0]: COPE = 1 x + 0 x =
[1 -1]: COPE = 1 x + -1x = -
• Test null hypothesis that COPE=0
t-contrasts
€
t =COPE
std(COPE)
��1��2
��1��2
t-statistic:
��1
��1��2
![Page 39: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/39.jpg)
t =COPE
std(COPE)
[1 0]
t-contrasts
Depends on
The Model and the Residual Error,the Contrast�
![Page 40: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/40.jpg)
t =COPE
std(COPE)
[1 0]
t-contrasts
The Model & the Contrast and the Residual Error�
const�}
![Page 41: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/41.jpg)
t-contrasts
• [1 0] : EV1 only (i.e. Generation vs rest) • [0 1] : EV2 only (i.e. Shadowing vs rest)
![Page 42: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/42.jpg)
[1 0]
t-contrasts
Model
Contrast weight vector:
Asks the question: Where do we need this regressor to model the data, i.e. what parts of the brain are used when seeing nouns and generating related verbs?
Time �
1.04�.10
��1
�2
![Page 43: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/43.jpg)
[1 0]COPE = 1� 1.04 + 0��0.10 = 1.04
COPE = =
t-contrasts
Contrast weight vector:
Model
Time �
1.04�.10
�
�1
�2
�1
![Page 44: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/44.jpg)
=t =COPE
std(COPE)=
t-contrasts
Model
Time �
1.04�.10
�
�1
�2
�
![Page 45: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/45.jpg)
t-contrasts
• [1 0] : EV1 only (i.e. Generation vs rest) • [0 1] : EV2 only (i.e. Shadowing vs rest)
• [1 1] : EV1 + EV2 (Mean activation)
![Page 46: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/46.jpg)
COPE =
�1.101.02
�
[1 1]COPE = 1� 1.10 + 1� 1.02 = 2.12
t-contrasts
Contrast weight vector:
Model
�2Time
�1
�2�1
= +
![Page 47: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/47.jpg)
=t =COPE
std(COPE)=
t-contrasts
Model
�
�1.101.02
��2Tim
e
�1
![Page 48: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/48.jpg)
t-contrasts
• [1 0] : EV1 only (i.e. Generation vs rest) • [0 1] : EV2 only (i.e. Shadowing vs rest)
• [1 1] : EV1 + EV2 (Mean activation)
• [-1 1]: EV2 - EV1 (More activated by Shadowing than Generation)
• [1 -1]: EV1 - EV2 (More activated by Generation than Shadowing (t-tests are directional))
![Page 49: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/49.jpg)
COPE = =
COPE = 1� 1.04� 1��0.10 = 1.14[1 �1]
�
t-contrasts
Contrast weight vector:
Model
Time �
1.04�.10
�
�1
�2
�1 �2
![Page 50: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/50.jpg)
=t =COPE
std(COPE)=
t-contrasts
Model
Time �
1.04�.10
�
�1
�2
�
![Page 51: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/51.jpg)
�2
�1t-contrasts
[1 �1]Why instead of [1 0] ?
Time �
1.101.02
�
=-
=
[1 �1]
=
[1 0]
![Page 52: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/52.jpg)
F-contrasts
We have two conditions: Word Generation and Shadowing
We want to know: Is there an activation to any condition?
⇥1 0
⇤- FIrst we ask: Is there activation to Generation?
![Page 53: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/53.jpg)
⇥1 0
⇤⇥0 1
⇤
F-contrasts
We have two conditions: Word Generation and Shadowing
We want to know: Is there an activation to any condition?
- Then we ask: Is there activation to Shadowing?
![Page 54: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/54.jpg)
1 00 1
�
F-contrasts
We have two conditions: Word Generation and Shadowing
We want to know: Is there an activation to any condition?
- Then we add the OR
![Page 55: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/55.jpg)
1 00 1
�
F-contrasts
We have two conditions: Word Generation and Shadowing
We want to know: Is there an activation to any condition?
- Then we add the OR
Is there an activation to any condition?
Is equivalent to:
Does any regressor explain the variance in the data?
![Page 56: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/56.jpg)
F-contrasts
Data
Full Model
&
![Page 57: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/57.jpg)
F-contrasts
Fit Model Estimate Residuals
Full Model
SSE
![Page 58: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/58.jpg)
F-contrasts
SSE
Fit Model Estimate Residuals
Full Model
Reduced Model
SSR
F =SSR � SSE
SSE= -
[0 1][1 0]
![Page 59: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/59.jpg)
F-contrasts
Full Model
F =SSR � SSE
SSE=
-
=
Reduced Model
=
![Page 60: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/60.jpg)
F-contrasts
- Two conditions: A,B
- Is any condition significant?
- Set of COPEs form an F-contrast
- Or: “Is there a significant amount of power in the data explained by the combination of the COPEs in the F-contrast?”
- F-contrast is F-distributed
![Page 61: Single-Session Analysis](https://reader035.vdocuments.site/reader035/viewer/2022072910/62e2e82b4cc0c558fb382b38/html5/thumbnails/61.jpg)
Summary
• The GLM is used to summarise data in a few parameters that are pertinent to the experiment.
• GLM predicts how BOLD activity might change as a result of the experiment.
• We can test for significant effects by using t or f contrasts on the GLM parameters
That's all folks